IIRC Leno was criticised for some clangers in his 1st season with us based upon his not catching the ball and trying to push it away, which then went to opposition players who then scored. I also recall there being similar issues pre-COVID, but his saves have been spectacular. He has looked suspect in traffic under a high ball, whereas Martinez has been more effective in his control of the area and under the highball.
Thus far other than the incident v LFC I don't think Martinez has actually committed any GK errors, although his positioning was out in one instance where the ball hit the far post and rebounded to safety.
Leno may be the better shot stopper but Martinez seems to be more in being the style of GK to play out from the back in a possession based system. As such IMO that gives him the starting position until he is not good enough and/or Leno wins it back.